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The conformation of single bottlebrush polymers is heavily influenced by their surrounding environment. 

In type systems with dependency tracking, programmers can assign an ordered set of levels to computations and prevent information flow from high-level computations to the low-level ones. The key notion in such systems isindistinguishability: a definition of program equivalence that takes into account the parts of the program that an observer may depend on. In this paper, we investigate the use of dependency tracking in the context of dependently-typed languages. We present the Dependent Calculus of Indistinguishability (DCOI), a system that adopts indistinguishability as the definition of equality used by the type checker. DCOI also internalizes that relation as an observer-indexed propositional equality type, so that programmers may reason about indistinguishability within the language. Our design generalizes and extends prior systems that combine dependency tracking with dependent types and is the first to support conversion and propositional equality at arbitrary observer levels. We have proven type soundness and noninterference theorems for DCOI and have developed a prototype implementation of its type checker. 

The orientation of chains within polymeric materials influences their electrical, mechanical, and thermal properties. While many techniques can infer the orientation distribution of a bulk ensemble, it is challenging to determine this information at the single-chain level, particularly in an environment of otherwise identical polymers. Here, we use single-molecule localization microscopy (SMLM) to visualize the directions of chains within spin-coated polymer films. We find a strong relationship between shear force and the degree and direction of orientation, and additionally, we reveal the effects of chain length and solvent evaporation rate. This work utilizes single-chain resolution to observe the important, though often overlooked, property of chain orientation in the common fabrication process of spin-coating. 

Although the behavior of single chains is integral to the foundation of polymer science, a clear and convincing image of single chains in the solid state has still not been captured. For bottlebrush polymers, understanding their conformation in bulk materials is especially important because their extended backbones may explain their self-assembly and mechanical properties that have been attractive for many applications. Here, single-bottlebrush chains are visualized using single-molecule localization microscopy to study their conformations in a polymer melt composed of linear polymers. By observing bottlebrush polymers with different side chain lengths and grafting densities, we observe the relationship between molecular architecture and conformation. We show that bottlebrushes are significantly more rigid in the solid state than previously measured in solution, and the scaling relationships between persistence length and side chain length deviate from those predicted by theory and simulation. We discuss these discrepancies using mechanisms inspired by polymer-grafted nanoparticles, a conceptually similar system. Our work provides a platform for visualizing single-polymer chains in an environment made up entirely of other polymers, which could answer a number of open questions in polymer science.